Supporting Information. Progressive Micro-Modulation of Interlayer Coupling in. Stacked WS 2 /WSe 2 Heterobilayers Tailored by a. Focused Laser Beam

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1 Supporting Information Progressive Micro-Modulation of Interlayer Coupling in Stacked WS 2 /WSe 2 Heterobilayers Tailored by a Focused Laser Beam Yayu Lee^, Zhenliang Hu^,, Xinyun Wang^,, Chorng-Haur Sow^, * ^Department of Physics, National University of Singapore, 2 Science Drive 3, Singapore Center For Advanced 2D Materials and Graphene Research Center, National University of Singapore, 6 Science Drive 2, Singapore of corresponding author: physowch@nus.edu.sg S-1

2 Section A: Estimation of the electric field between electron-hole pair in intralayer excitons Using the simplified Wannier-Mott exciton model 1. This model is relevant due to the presence of a relatively weaker electrostatic screening effects in 2D materials, where the electron-hole pair can be treated to behave similar to an isolated hydrogen atom system with the following quantized energy levels. E n = μ m 0 1 ε r 2 R H n 2 (1) Where E n : Quantized binding energy levels of the Wannier-Mott exciton, μ: Effective reduced mass of the electron-hole pair, m o : Rest mass of an electron, R H : Rydberg energy (13.6 ev), ε r : Relative permittivity constant, n: Quantum number. Using the parameters computed by Pedersen et al. (where the effective masses of the electron and hole in the out-of-plane direction, are and respectively, and their out-of-plane dielectric constants are 7.62 and 7.07 for the WS 2 and WSe 2 monolayers respectively 2 and fitting them into equation (1), we can obtain a binding energy value of approximately 0.37 ev for intralayer excitons in WS 2 and 0.33 ev for that in WSe 2. The binding energy values obtained here agree well with that found in both theoretical and experimental studies in other scientific papers, in which the exciton binding energies in these materials range from about 0.2 to 0.5 ev 3-5. S-2

3 Subsequently, using the following relation in (2) which is based on the electrostatic model, these values can then be translated into an electric field of approximately Vm -1 and Vm -1 for the intralayer WS 2 and WSe 2 excitons respectively. EF = 4πε 2 0ε r E n (2) e 3 Where e: unit charge ( C) ε 0 : Vacuum permittivity constant ( Fm 1 ) ε r : Relative permittivity n: Quantum number (n taken to be 1 here) E n : Exciton binding energy E F : Electric field S-3

4 Figure S1: A schematic diagram of the focused laser beam set-up which consists of a laser source and a system of mirrors and beam splitters that focuses and directs the laser onto the sample placed onto the motorized stage. In order for the laser treatment to be carried out, the motorized stage is programmed to move at a specified speed along a certain direction such that the laser scans across the required region of the sample. The laser modification set-up is also equipped with a miniature gas chamber shown in the box that allows modification to be carried out in a controlled environment (the gas inlet and outlet pipes enable a low vacuum to be reached and allows other types of inert gases such as He to be flushed through the chamber and across the sample). The chamber is sealed by a quartz plate as labelled in the diagram. S-4

5 Figure S2: a) Optical microscope image of the exfoliated WS 2 replicated here for easy reference b) AFM image scan of the WS 2 monolayer on SiO 2 substrate. The region at which the AFM scan is conducted corresponds to the area indicated by the white rectangle in image a). c) The height profile of the WS 2 monolayer on SiO 2 substrate which was taken along the white line indicated in image b). S-5

6 Figure S3: Optical microscope image of a) The WSe 2 sample that was being exfoliated onto a PDMS substrate. Figure S4: PL spectrum (incident laser wavelength: 532nm) obtained for the exfoliated WSe 2 sample. S-6

7 Figure S5: Raman spectrum (incident laser wavelength: 532nm) of the exfoliated WSe 2 which was transferred onto 300 nm SiO 2 substrate. S-7

8 Figure S6: Normalised PL spectra of the sample at various stages of the experiment separated to display the (a) WS 2 and (b) WSe 2 peaks independently. Figure S7: Schematic diagram of the charge transfer process in the WS 2 /WSe 2 heterostructure. 1. Photoexcitation occurs in the independent monolayers, creating electronhole pairs. 2. Charge transfer then occurs; the electrons then move towards the WSe 2 monolayer, while holes move towards the WS 2 monolayer 3. A spatial separation of the electron-hole pairs results, as indicated by the dashed oval. S-8

9 Figure S8: a) OM image of the heterostructure. The 1L-WSe 2 and 1L-WS 2 are outlined by the blue and black dashed lines. b) Zoomed-in OM image of the unmodified heterostructure. During the transfer process, fragmentation of the top 1L-WSe 2 occurred, causing the heterostructure to break up into three separate regions, as indicated in the image. For consistency purposes, our single spectroscopy measurements were carried out at location 1 throughout the various stages of the experiment. Figure S9: Raman mapping images (selected range: cm -1, i.e. the window for WSe 2 ) of the heterostructure: (a) before laser irradiation (c) after two laser irradiation processes (15 and 25 mw). Corresponding Raman mapping images for a different spectral range of cm -1, i.e. the window for WS 2, are shown in (b) and (d) respectively. S-9

10 Figure S10: Overview summary results for another sample to show that we have reproduced the results on a number of samples. a) OM image of the heterobilayer before laser modification. The blue dash lines outline the position of the top WSe 2 layer and the black dashed lines outline the position of the bottom WS 2 monolayer. b) Its corresponding FM image (exposure time: 1s) c) AFM image of sample before modification. The three different coloured dashed lines (green, yellow and red) represent the different fragmented segments of the heterobilayer structure, labelled 1,2 and 3 respectively. The corresponding OM, FM and AFM S-10

11 scan images for the modified heterostructure are shown in d), e) and f) respectively. g) Raman spectrums (incident laser wavelength: 532 nm) of the heterostructure taken at the various stages of the experiment at location 2. h) PL spectrums of the heterostructure. i) Evolution of the interlayer separation before and after laser irradiation at different successive laser powers of the three different locations of the heterostructure. The following information was extracted from the height profiles taken along the orange lines indicated in figures c) and f). Figure S11: Overview summary results for another sample to show that we have reproduced the results on a number of samples. a) OM images of the heterostructure before and b) after laser modification. FM (exposure time: 1s) images of the heterostructure c) before and d) after laser modification. The blue and black dashed lines demarcate the positions of the monolayer WSe 2 and WS 2 materials respectively. e) PL spectrums collected for the overlapped region S-11

12 before and after laser modification. f) Raman spectrums of the heterostructure before and after laser modification. Figure S12: AFM scans of heterostructure a) before and b) after laser modification. Height profiles taken along the orange lines indicated in a) and b), which are shown in c) and d) respectively S-12

13 Figure S13: AFM scan images obtained for the WS 2 /WS 2 homobilayer, a) before and b) after laser irradiation. The fragmented section of the homobilayer region that experienced a change in its optical properties is being outline in yellow. The height profiles taken before and after laser irradiation are shown in images c) and d) respectively. The height profiles were taken at the positions indicated by the yellow lines in images a) and b). The interlayer separation values shown in the figure were attained by taking the height difference between the two blue crosses indicated in c) and d). The positions of these two blue crosses correspond to that in images a) and b), where the first cross is positioned at the top of the bottom WS 2 layer, while the second cross is positioned at the top of the WS 2 monolayer above. S-13

14 REFERENCES: 1. Kittel, C., Introduction to Solid State Physics. 8th ed.; Wiley: Hoboken, NJ, 2005; p Thomas Garm, P.; Simone, L.; Kristian, S. T.; Héctor, M.; Branislav, K. N., Exciton Ionization in Multilayer Transition-Metal Dichalcogenides. New J. Phys. 2016, 18 (7), Chernikov, A.; Berkelbach, T. C.; Hill, H. M.; Rigosi, A.; Li, Y.; Aslan, O. B.; Reichman, D. R.; Hybertsen, M. S.; Heinz, T. F., Exciton Binding Energy and Nonhydrogenic Rydberg Series in Monolayer WS 2. Phys. Rev. Lett. 2014, 113 (7), Berkelbach, T. C.; Hybertsen, M. S.; Reichman, D. R., Theory of Neutral and Charged Excitons in Monolayer Transition Metal Dichalcogenides. Phys. Rev. B 2013, 88 (4), He, K.; Kumar, N.; Zhao, L.; Wang, Z.; Mak, K. F.; Zhao, H.; Shan, J., Tightly Bound Excitons in Monolayer WSe 2. Phys. Rev. Lett. 2014, 113 (2), S-14